1. Introduction

Coherent anti-Stokes Raman scattering (CARS) spectroscopy and microscopy attract significant attention in that it allows label-free, chemically-selective and, potentially, sensitive imaging and sensing [1]. To achieve efficient nonlinear optical interaction, picosecond pulses are typically employed, since the spectral bandwidth of such pulses perfectly matches a typical linewidth for a Raman transition of a molecule in solution, i.e. a few wavenumbers. A growing number of applications requires simultaneous recording of a broadband CARS spectrum, especially, in the Raman fingerprint region spanning from 800 to 1800 cm⁻¹, to achieve a comprehensive chemical assessment of the sample under study [2–5]. Those measurements are often difficult to perform because of the non-resonant instantaneous electronic four wave mixing (FWM) interaction which interferes with a resonant CARS signal generation and results in a complex spectral shape of the recorded spectrum. Various methods and techniques have been proposed and used extensively either to eliminate or to suppress the FWM background, thus increasing the specificity of the CARS spectroscopy. These techniques range from polarization control [6], temporal pulse shaping [7], heterodyning [8], and data processing [9, 10]. Each of those approaches has its own advantages and shortcomings, and the purpose of this report is to introduce yet another concept which utilizes the cascaded nonlinear optical interaction in ${\chi }^{\left(2\right)}$ materials. In biological systems, collagen-rich tissue can be considered as a representative example of such material.

In noncentrosymmetric crystals, the cascaded quadratic nonlinearity under conditions of large phase mismatch is proportional to the phase mismatch factor Δk, where k is the wave vector [11]. It can be positive or negative depending on the phase mismatch. The material Kerr third-order nonlinearity is usually positive [12]. As a result, the effective total third-order nonlinearity can change its sign as one varies the phase matching angle. The cascaded quadratic nonlinearity and the third-order nonlinearity in nonlinear crystals have been studied extensively in the context of measuring the third-order nonlinear tensor elements [13, 17], soliton compression [11] and high-intensity third-harmonic generation [14], to name a few.

We have recently proposed and experimentally validated a new technique for the FWM background suppression [15]. It is based on the interaction of nonlinear optical signals which are generated from the Kerr third-order nonlinear process and the cascaded quadratic process. In a typical CARS setup, where both the pump, ω_p, and the Stokes, ω_s, beams are focused into a nonlinear crystal, the nonlinearities from the electronic non-resonant Kerr effect, the resonant coherent Raman effect, and the cascaded quadratic processes coexist. In our early approach [15], the first process is the second-harmonic generation (SHG) of the pump beam which results in a signal at frequency 2 ω_p. The second process is the difference-frequency generation (DFG) between the second harmonic of the pump beam, 2 ω_p, and the Stokes beam, ω_s, which leads to a new wave at frequency 2ω_p- ω_s, which is the same as the CARS signal frequency. We showed that by tuning the crystal angle, the cascaded second-order signal can be tuned out of phase with the non-resonant FWM background. This homodyne CARS process thus provides an alternative way of eliminating instantaneous FWM background.

Unfortunately, the above scheme only works when the polarizations of the two beams (pump and Stokes) are perpendicular to the optical axis of a crystal, and the type I phase matching (oo$\to$e) is employed. When the polarization of the pump and Stokes beams are both e-polarized, the ee$\to$o interaction is highly phase mismatched. Therefore, the main cascaded channel would be ee$\to$e interaction, which can never be phase matched. Consequently, there was no cascaded quadratic process observed, and the lineshape stayed unchanged as we varied the angle.

In this report, we explore two of the four most widely used nonlinear optical crystals, potassium titanyl phosphate (KTP) [16, 17] and lithium niobate (LiNbO₃) [18, 19]. Furthermore, we investigate the possibility of heterodyning CARS signal at the interface of two media – isopropyl alcohol and nonlinear crystal, LiNbO₃.

2. Experimental setup

The experimental setup is similar to the one used in the previous work [14]. Briefly, we employed a home-built MHz-rate diode-pumped Nd:YVO₄ oscillator amplified by a diode-pumped two-stage Nd:YVO₄ amplifier, which produced 10 µJ, 8 ps pulses at the wavelength of 1064 nm and an average power as high as 8 W [20]. The output was split by a polarizing beam splitter (PBS). One part was focused into a single-mode GeO₂ doped fiber to generate supercontinuum (SC) extending from 1100 nm to 1600 nm [21]. This supercontinuum radiation served as a broadband Stokes pulse (ω_s), whereas the rest of the fundamental radiation (ω_p) at 1064 nm was used as a narrow band (<5 cm⁻¹) pump/probe pulse to achieve a simultaneous excitation of all Raman modes in the spectral region of interest (200–3,000 cm⁻¹). Half waveplates in a combination with polarizing cubes were used to attenuate the beams to avoid the saturation of nonlinear processes. The SC and the pump/probe beams were combined by a dichroic mirror (Semrock, Inc) collinearly and then focused into a nonlinear crystal using an achromatic aspheric lens (Thorlabs, Inc.).

3. CARS utilizing cascaded nonlinear interactions in KTP and LBO

KTP is widely used as the type II nonlinear optical crystal in the XY and XZ planes. With a crystal cut at φ = 23.4 degrees in the XY plane for the SHG of the 1064-nm radiation, we find that by letting the pump and the Stokes waves be both either o or e waves leaves a possibility for all types of nonlinear interactions to be excited in each step of the cascading interaction. In the XY plane, the o wave aligned with the crystallographic z-axis and the e wave – in the XY plane (see inset of Fig. 1). The possible nonlinear interactions, thus, are: o,o→2o with a nonlinear coefficient d₃₃; o, e→2e (nonlinear coefficient: d₁₅sin²φ + d₂₄cos²φ), and e,e→2o (nonlinear coefficient: d₃₁sin²φ + d₃₂cos²φ).

 

Fig. 1 Experimentally measured CARS spectra of the KTP crystal (φ = 23.4 degree) generated under different phase matching conditions. Both the pump/probe and the Stokes beams are either o-polarized (red dotted line) or e-polarized (black solid line). Inset: the KTP crystal axis and the direction of the e- and o- polarized light.

Download Full Size | PDF

Maintaining single o- or e- polarization removes any phase matched SH wave independent of the crystal φ orientation. We note that even with a strong phase mismatch in each of the cascading steps o,o→2o, and 2o,o→o, a large value of nonlinear coefficient d₃₃ is sufficient to overcompensate for the χ⁽³⁾ contribution to the CARS signal. Most notably, the material’s birefringence ensures that the cascaded contribution stays negative, i.e. has the same sign as the background χ⁽³⁾ of the crystal. This is illustrated in Fig. 1, where different polarizations of the pump and the Stokes beams are used. Note that the CARS spectral line-shape is dramatically transformed, if the polarizations of the incoming beams change to the e-polarization. This is a quite remarkable observation, since it allows manipulating the relative contribution and relative phase of the non-resonant background by simply varying the incident polarization of the pump/probe and the Stokes beams.

We further explored how coherent Raman, FWM and cascaded quadratic processes interact in a LiNbO₃ crystal. A Y-cut LiNbO₃ crystal allows the type I phase matching for the fundamental wavelength above 1.18 μm; the dispersion properties are often being tailored by doping, with most popular dopant being Mg. In our studies, we used a non-doped congruent LiNbO₃ Y-cut wafer with the polarizations of the pump and the Stokes waves either perpendicular or parallel to the optical axis oriented in the plane of the wafer’s surface. The first case corresponds to the type I phase matching for the pump wave or the type I sum-frequency generation between the pump and the Stokes waves for the first step of the cascaded interaction. We note that, for the direction of the beam propagation along the Y axis with both slow pump and Stokes waves, only a single non-vanishing channel, which corresponds to the o,o→2e interaction for the up-conversion and the 2e,o→o interaction for the down-conversion step, is possible. In the second case, of parallel polarizations, the nonlinear coefficient d₃₃ is the only effective nonlinear coefficient responsible for the up- and down- conversion stages for three extraordinary waves, and none of the steps are possible to be phase matched with the existing birefringence. The lack of flexibility in controlling the phase-matching results in an obvious difficulty of suppressing the non-resonant background, as it is illustrated in Fig. 2 for different polarizations of the incoming beams.

 

Fig. 2 The experimentally measured CARS spectra generated in the LiNbO₃ crystal under different phase matching conditions. Both the pump/probe and the Stokes beams are either o-polarized (red dotted line) or e-polarized (black solid line). Inset: the Y-cut LiNbO₃ crystal axis and the direction of the e- and o- polarized light.

Download Full Size | PDF

4. CARS background suppression utilizing cascaded nonlinear interactions at the interface of two media

To add a much-needed flexibility for the non-resonant CARS background suppression, we utilized the interface between two media – isopropyl alcohol and the same wafer of the LiNbO₃ crystal, as the one discussed in the previous section. Such system has an intrinsic advantage with respect to the single-medium system because it allows the heterodyning of the CARS signal generated in one medium through the interference with the CARS signal generated in the other medium. The relative contribution of each of those two CARS signals can be conveniently controlled by moving the focal spot across the interface, which is normally done in 3D CARS microscopy imaging [1]. When the polarization of the incoming beams is perpendicular to c-axis of the LiNbO₃ crystal, the spectrum shifts from the Raman peak of a pure isopropyl alcohol solution at 820 cm⁻¹ [22] to the 883 cm⁻¹ Raman line of LiNbO₃ [23] as we gradually shift the focus from the bulk of isopropyl alcohol solution to the bulk of the LiNbO₃ crystal with a few μm step. The rest of the CARS spectral shape remains relatively unchanged, as it is illustrated in Fig. 3.

 

Fig. 3 The experimentally measured CARS spectra generated at or near the interface between isopropyl alcohol solution and LiNbO₃ crystals, as the position of the focus is moved from the bulk of isopropyl alcohol (red solid line) to the bulk of LiNbO₃ crystal (green dotted line) with the incident light polarizations perpendicular to the c-axis of the LiNbO₃ crystal.

Download Full Size | PDF

When we switch the polarization of the incident beams to be parallel to the c-axis of the LiNbO₃ crystal, we observed a dramatically different behavior (see Fig. 4). At the high frequency shift range, where only isopropyl alcohol has Raman resonances, the interference of the FWM signal in the liquid and cascaded quadratic nonlinear signal in the LiNbO₃ crystal leads to the substantial spectral shape variations. As a result a significant suppression of the non-resonant can be achieved at a certain location across the interface (green line in Fig. 4). This example, which uses the externally controlled polarization and the spatially controlled heterodyning, demonstrates the untapped great potential for the background free CARS microscopy.

 

Fig. 4 Experimentally measured CARS spectra generated at or near the interface between isopropyl alcohol and the LiNbO₃ crystal with the incident light polarizations parallel to the c-axis of the LiNbO₃ crystal. The position of the focus is moved from the bulk of isopropyl alcohol (pink solid line) to the bulk of LiNbO₃ crystal (red dot-dashed line). Two frequency ranges are plotted with different vertical scales to emphasize appearance of the non-resonant background suppression of isopropyl alcohol line at around 1460 cm⁻¹ (green dashed curve).

Download Full Size | PDF

6. Summary

We have experimentally explored the interaction between the instantaneous FWM process and the cascaded quadratic nonlinearity in commonly used nonlinear crystals for the purpose of background suppression of instantaneous four wave mixing background in CARS spectroscopy. We have also found that it is possible to realize background-free heterodyne CARS microspectroscopy by utilizing cascaded quadratic nonlinear interactions at the interface between the object under study and a nonlinear crystal.